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Random Models in Arithmetic and Spectral Theory

Objective

The proposal studies deterministic problems in the spectral theory of the Laplacian and in analytic number theory by using random models. I propose two projects in spectral theory on this theme, both with a strong arithmetic ingredient, the first about minimal gaps between the eigenvalues of the Laplacian, where I seek a fit with the corresponding quantities for the various conjectured universality classes (Poisson/GUE/GOE), and the second about curvature measures of nodal lines of eigenfunctions of the Laplacian, where I seek to determine the size of the curvature measures for the large eigenvalue limit. The third project originates in analytic number theory, on angular distribution of prime ideals in number fields, function field analogues and connections with Random Matrix Theory, where I raise new conjectures and problems on a very classical subject, and aim to resolve them at least in the function field setting.

Call for proposal

ERC-2017-ADG
See other projects for this call

Funding Scheme

ERC-ADG - Advanced Grant

Host institution

TEL AVIV UNIVERSITY
Address
Ramat Aviv
69978 Tel Aviv
Israel
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 840 625

Beneficiaries (1)

TEL AVIV UNIVERSITY
Israel
EU contribution
€ 1 840 625
Address
Ramat Aviv
69978 Tel Aviv
Activity type
Higher or Secondary Education Establishments